Can butterfly's and crickets live together?

Butterflies do not provide parental care for their offspring, and in most cases, by the time the caterpillars hatch from the eggs, the adult butterfly that laid the eggs is either dead or has moved on. The whole reason complete metamorphosis (changing from a caterpillar to a butterfly) exists is so the adults and young of the species do NOT have to occupy the same niche and compete with one another. That doesn't mean you'll never see a caterpillar and butterfly in the same place at the same time, but if you do see this, it's purely coincidence that they happened to be there. They don't care about each other; the caterpillar just crawls along looking for food while the butterfly searches for places to lay eggs or find a mate.